Title: The Topology of Data: from String Theory to Cosmology to Phases of Matter
Abstract: We are faced with an explosion of data in many areas of physics, but very so often, it is not the size but the complexity of the data that makes extracting physics from big datasets challenging. As I will discuss in this talk, data has shape and the shape of data encodes the underlying physics. Persistent homology is a tool in computational topology developed for quantifying the shape of data. I will describe how topological data analysis (TDA) can be used to 1) identify the structure of the string landscape, 2) constrain cosmological parameters from CMB measurements and large scale structure surveys, and 3) detect and classify phases of matter. Persistent homology condenses these datasets into their most relevant (and interpretable) features, so that simple statistical analyses are sufficient for extracting relevant physics. We further illustrate that TDA can be used in conjunction with machine learning algorithms to develop statistical inference models.
Organised by
Judit Prat, Ivan Khaymovich, Dhruba Mitra, Florian Niedermann, Alexander Balatsky